Cycles Render - Glass Shader: Some faces are rendered black
This has a rather simple reason.
Your edges are too sharp, and Blender doesn't like it.  

Solution
1) Apply a small bevel to your edges
2) Set shading to smooth
3) Boom. You're done.  

Bevel outer edges.
This will take care of those sharp edges, and also make Blender happy.
4 segments are enough, set the width as desired.


Set smooth shading.
This will smooth out the normals, so the transition is more gradual.


Looks good!